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In Chapter 14.4 (p. 664) of the book Pattern Recognition and Machine Learning by Bishop, it is mentioned that tree-based models are more widely used in Medical Diagnosis.

Apart from giving better performance, is there a human-centric reason for this trade-off as medical diagnosis is mainly performed by a human?

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Either you missed it or I don't fully understand why you were confused when you asked this question, but the same Bishop argues (in the same sentence where he says what you are wondering about) why tree-based models are popular in fields such as medical diagnosis.

A key property of tree-based models, which makes them popular in fields such as medical diagnosis, for example, is that they are readily interpretable by humans because they correspond to a sequence of binary decisions applied to the individual input variables. For instance, to predict a patient's disease, we might first ask "is their temperature greater than some threshold?". If the answer is yes, then we might next ask “is their blood pressure less than some threshold?". Each leaf of the tree is then associated with a specific diagnosis.

Nowadays, with the successes of neural networks (for example, in Go, Atari, image classification and segmentation, and even machine translation), which are not easily interpretable (so they are known as black-box models), there are always more studies/research on interpretable models or techniques to interpret black-box models, such as neural networks. You can take a look at this answer for a list of explainable/interpretable AI approaches that have been developed. This post contains many answers that further motivate the need for explainble AI.

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One possible reason may have something to do with the scrutability of models, as described in the first few paragraphs of this article. It presents a case study of a hospital whose policy was to send asthma sufferers to an intensive care unit; the intensive care meant they were less likely to develop pneumonia and therefore the data showed that people with asthma were less likely to have pneumonia.

Essentially, since machine learning models learn false relationships if the data are in any way flawed, it is beneficial to be able to "debug" them. The processes by which decision trees make their decisions, and the reasons for making them, are more readily visible than in other models - particularly neural networks - which makes errors such as the example given in the article more likely to be picked up and corrected.

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I myself working on similar product for Medical Diagnosis. The reason for it is we as ML engineer, generally try to replicate, how human approach any problem into mathematical model and build library on top of it to use it in application.

So, how Doctor approach to any specific decision of diagnosis, based on symptoms. Mainly symptoms are in two form True or False, you have it or not.

Now we just need to replicate doctors approach to make decision, But yes to extract those symptoms from raw data in the form of text, image of sound we need to use other classifier and clustering models.

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